SURFACE AREA AND VOLUME OF A CUBE EXAMPLES

Let the side of a cube be 'a' units.

Then,

(i) The Total Surface Area (T.S.A)  =  6a2 square units.

(ii) The Lateral Surface Area (L.S.A)  =  4a2 square units.

(ii) Volume of cube  =  a3 cubic units.

Solved Examples

Example 1 :

The volume of the cube is 125 dm3. Find its side.

Solution :

Volume of cube  =  125 dm3

a3  =  125

a3  =  53

a  =  5 dm

So, side length of cube is 5 dm.

Example 2 :

A container is in the shape of a cube of side 20 cm. How much sugar can it hold?

Solution :

In order to find the quantity of sugar that the container can hold, we have to find the volume of container.

Side length of cubical container  =  20 cm

Volume of container  =  a3

=  (20)3

=  8000 cm3

Example 3 :

A cubical tank can hold 64,000 litres of water. Find the length of the side of the tank.

Solution :

Let a be the side of the cubical tank. Volume of the tank is 27,000 litres. So,

V  =  a3  =  (27000/1000)

a3  =  27

a  =  ∛27

a  =  3 m

Example 4 :

Three metallic cubes of side 3 cm, 4 cm and 5 cm respectively are melted and are recast into a single cube. Find the total surface area of the new cube.

Solution :

Side length of 1st cube  =  3 cm

Side length of 2nd cube  =  4 cm

Side length of 3rd cube  =  5 cm

Volume of 1st, 2nd and 3rd cube  =  33 + 43 + 53

=  27 + 64 + 125

=  216

a3  =  216

a3  =  63

a  =  6 cm

Total surface area of new cube  =  6a2

=  6(6)2

=  6(36)

=  216 cm2

So, total surface area of new cube 216 cm2

Example 5 :

Find the L.S.A, T.S.A and volume of a cube of side 5 cm.

Solution :

Lateral surface area (L.S.A)  =  4a2

=  4(52 ) = 100 sq. cm

Total surface area (T.S.A)  = 6a2

=  6 (52 )

=  150 sq. cm

Volume of cube  =  a3

=  53

=  125 cm3

Example 6 :

Find the length of the side of a cube whose total surface area is 216 square cm.

Solution :

Let a be the side of the cube.

Given that T.S.A = 216 sq. cm

6a2  =  216

a2  =  216/6

a2  =  36

a  =  √36

a  =  6 cm

Example 7 :

A cube has a total surface area of 384 sq. cm. Find its volume.

Solution  :

Let a be the side of the cube. Given that T.S.A = 384 sq. cm

6a2 = 384

a2  =  384/6

a2  =  64

a  =  64  =  8 cm

So, volume is

=  a3

=  83

=  512 cm3

Example 8 :

If the lateral surface area of a cube is 900 cm2, find the length of its side.

Solution :

Lateral surface area of cube  =  4a2

4a2  =  900

a2  =  900/4

a2  =  225

a  =  √225

a  =  15 cm

So, the side of cube is 15 cm.

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